A5.0-kg hollow cylinder of radius 0.37m rotates freely about an axle that runs through its center and along its long axis. a cord is wrapped around the cylinder and is pulled straight from the cylinder with a steady tensile force of 50 n . as the cord unwinds, the cylinder rotates, with no slippage between cord and cylinder.
a- calculate the work done by the tensile force as the cylinder rotates through 1000 rad
b- if the cylinder starts from rest, calculate its rotational speed after it has rotated through 1000 rad .

A-18500J

B-232.5 rad/s

Explanation:

A- As the cylinder rotates through 1000rad, it sweeps a distance of

So the work, which is distance times force, of the tension done on the cylinder through that distance is

W = Td = 50 * 370 = 18500  J[/tex]

B- The torque that exerts on the cylinder by the tension is

To = TR = 50*0.37 = 18.5 Nm

As the cylinder is hollow, its moments of inertia is

The torque is generating an angular acceleration of:

The time it takes to go from rest to 1000 rad

Therefore the final rotational speed is

0.55x745.7j and a calculator

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